717896
Description
Mind Map by james_hobson, updated more than 1 year ago
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Created by james_hobson
about 10 years ago
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Indices and Surds
- Indices
- Multiplication Rule
- x^a * x^b = x^a+b
- e.g. 2^2 * 2^3 = 2^5 = 32
- x^a * x^b = x^a+b
- Division Rule
- x^a / x^b = x^a-b
- e.g. 2^3 / 2^2 = 2^1 = 2
- x^a / x^b = x^a-b
- Power on Power Rule
- (x^a)^b = x^a*b
- e.g. (2^3)^2 = 2^3*2 = 2^6 = 64
- (x^a)^b = x^a*b
- Power of Zero
- x^0 = 1
- e.g. 2^0 = 1
- x^0 = 1
- Negative Powers
- x^-a = 1/x^a
- e.g. 2^-2 = 1/2^2 = ¼
- x^-a = 1/x^a
- Fractional Indices
- x^a/b = (b√(x))^a
- e.g. 8^2/3 = (cube √(8))^2 = 2^2 = 4
- x^a/b = (b√(x))^a
- Multiplication Rule
- Surds
- Addition
- a*√(b) + c*√(b) = (a+c)*√(b)
- e.g. 4*√(7) + 3*√(7) = 7*√(7)
- a*√(b) + c*√(b) = (a+c)*√(b)
- Subtraction
- a*√(b) - c*√(b) = (a-c)*√(b)
- e.g. 4*√(7) - 2*√(7) = 2*√(7)
- a*√(b) - c*√(b) = (a-c)*√(b)
- Multiplication Rule
- √ab = √a * √b
- e.g. √2*4 = √2*√4 = 2√2
- √ab = √a * √b
- Division Rule
- √a/b = √a / √b
- e.g. √2/3 = √2 / √3
- √a/b = √a / √b
- Rationalising the Denominator
- a / √b * √b / √b = a√b / b
- e.g. 1 / √2 * √2 / √2 = √2 / 2
- e.g. 1 / √2 * √2 / √2 = √2 / 2
- a / b+√c * b-√c / b-√c = a(b-√c) / (b+√c)(b-√c)
- e.g. 1 / 2+√2 * 2-√2 / 2-√2 = 2-√2 / 4-2 = 2-√2 / 2
- e.g. 1 / 2+√2 * 2-√2 / 2-√2 = 2-√2 / 4-2 = 2-√2 / 2
- a / √b * √b / √b = a√b / b
- Addition
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